Problem: Solve the system of equations. $\begin{aligned} & 10x-9y = 24 \\\\ & y=x-2 \end{aligned}$ $ x=$
Explanation: We are given that $ y = {x-2}$. Let's substitute this expression into the first equation and solve for $x$ as follows: $ \begin{aligned} 10x-9{y}&=24\\\\ 10x-9\cdot({x-2})&=24\\\\ 10x-9x+18& = 24\\\\ x&=6\\\\ \end{aligned}$ Since we now know that $ x={6}$, we can substitute this value into the second equation to solve for $y$ as follows: $\begin{aligned} y &= {x}-2 \\\\ y&={6}-2\\\\ y&=4 \end{aligned}$ This is the solution of the system: $\begin{aligned} &x = 6 \\\\ &y=4 \end{aligned}$